A305600 G.f. A(x) satisfies: [x^k] (1+x)^(n^2) * A(x) = 0 for k = (n-1)^2 + 1 through k = n^2 for n >= 1.

1, -1, -2, 10, -25, 33, 57, -561, 2310, -7150, 18448, -39168, 55114, 41990, -726750, 3657006, -13846041, 44907185, -130605450, 347227650, -845335695, 1842623895, -3311675445, 3271798125, 9143639100, -77910795756, 356581496251, -1331363100907, 4430526577054, -13595755404934, 39119816049161, -106498829726801, 275433122695473, -676162020887697, 1563087628000497, -3329539580829865, 6175049600047825

Offset: 0

Author

Paul D. Hanna, Jun 13 2018

Keywords

• sign

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..2500

Programs

PARI

/* Informal code to generate terms */
{A=[1,-1]; for(i=1,400, A=concat(A,0); m=sqrtint(#A-2)+1; A[#A] = -polcoeff( (1+x +x*O(x^#A))^(m^2)*Ser(A),#A-1) ;print1(#A,","));A}
/* Show that the definition is satisfied: */
for(n=1,sqrtint(#A),print1(n": ");for(k=(n-1)^2+1,n^2,print1(polcoeff( (1+x+x*O(x^#A))^(n^2)*Ser(A) ,k),","));print(""))